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# Orders of magnitude exercise example 1

Video transcript

So we're told that Mount
Everest is 29,029 feet tall. Estimate Mount Everest's
height by rewriting it as a number in the form x times
10 to the y-th power feet, where x and y are
single-digit numbers. So let's think about
how we would do this. So x and y have to be
single-digit numbers. So if we were to write it
in scientific notation, we could write something
like, let's see, it would be 2.9029 times 10. And actually, I'm
going to be careful. Times I should write like that. I'll use this little caret sign. I'm pressing shift and
6 to get the caret sign. Times 10 to the-- and
I moved the decimal. Let's see, in order to
go from 2 to 20,000, I have to add 1, 2, 3, 4 zeroes,
so times 10 to the fourth. So that's what I would
do if they were just asking us to write it
in scientific notation. But they're not
asking us to write it in scientific notation. They're saying estimate
Mount Everest's height by writing it in
this form, where x and y are
single-digit numbers. So as I wrote it
right over here, 2.0929 is not a
single-digit number. 4 is a single-digit number. So at least I got
the y part right. But I need to write this
part, which, in this form, this would be the x. I need to write that as
a single-digit number. And the key is that they
want me to estimate. So if I were to estimate
2.9029, I would write that as 3. So I'm going to go with
3 times 10 to the fourth. And if I were to expand out
3 times 10 to the fourth, it would be 30,000 feet. So my estimate
seems pretty good. So let's check. There we go.